Modern Math

Permutation & Combination

Easy

How many signposts can be made using 6 different coloured symbols when any number of them can be posted at a time?

1988

1976

1966

1956

✅ Correct Option: 4

Since any number of symbols can be used:

Using 1 symbol: $^6C_1$ × $^1P_1 = 6 × 1$ ways

Using 2 symbols: $^6C_2$ × $^2P_2 = 15 × 2$ ways

Using 3 symbols: $^6C_3$ × $^3P_3 = 20 × 6$ ways

Using 4 symbols: $^6C_4$ × $^4P_4 = 15 × 24$ ways

Using 5 symbols: $^6C_5$ × $^5P_5 = 6 × 120$ ways

Using 6 symbols: $^6C_6$ × $^6P_6 = 1 × 720$ ways

Total = $6(1) + 15(2) + 20(6) + 15(24) + 6(120) + 1(720)$

= $6 + 30 + 120 + 360 + 720 + 720$

= $1956$

Therefore, 1956 different signposts can be made.

IPMAT Rohtak 2020

Five racquets need to be placed in three boxes. Each box can hold all the five racquets. In how many ways can the racquets be placed in the boxes so that no box can be empty if all racquets are different but all boxes are identical?

IPMAT Rohtak 2020

There are 12 copies of Beetles CDs, 7 copies of Pink Floyd CDs, 3 different CDs of Michael Jackson, and 2 different CDs of Madonna. Find the number of ways in which one or more than one CD can be selected?

IPMAT Rohtak 2020

Please calculate in how many ways can a platoon of sixteen soldiers be chosen out of a total of twenty soldiers for a surgical strike?

IPMAT Rohtak 2020

A box contains 2 white shirts, 3 black shirts, and 4 red shirts. In how many ways can 3 shirts be drawn from the box, if at least one black shirt is to be included in the draw?

IPMAT Rohtak 2020

Can you calculate in how many ways can 7 tennis players can be seated in a circular order?

IPMAT Rohtak 2020

Please calculate in how many ways can a set of five players be formed out of a total of ten players such that two particular players should be involved in each set?

How many signposts can be made using 6 different coloured symbols when any number of them can be posted at a time?

Solution

Related questions:

Keyboard Shortcuts

IPMAT Rohtak Past Year Questions (Topic-Wise)